A feedback (closed-loop) control system 10, as shown in Prior Art FIG. 1, is widely used to modify the behavior of a physical process, denoted as the plant 110, so it behaves in a specific desirable way over time. For example, it may be desirable to maintain the speed of a car on a highway as close as possible to 60 miles per hour in spite of possible hills or adverse wind; or it may be desirable to have an aircraft follow a desired altitude, heading and velocity profile independently of wind gusts; or it may be desirable to have the temperature and pressure in a reactor vessel in a chemical process plant maintained at desired levels. All these are being accomplished today by using feedback control, and the above are examples of what automatic control systems are designed to do, without human intervention.
The key component in a feedback control system is the controller 120, which determines the difference between the output of the plant 110, (e.g. the temperature) and its desired value and produces a corresponding control signal u (e.g., turning a heater on or off). The goal of controller design is usually to make this difference as small as possible as soon as possible. Today, controllers are employed in a large number of industrial control applications and in areas like robotics, aeronautics, astronautics, motors, motion control, thermal control, and so on.
Classic Controllers
Classic Control Theory provides a number of techniques an engineer can use in controller design. Existing controllers for linear, time invariant, and single-input single output plants can be categorized into three forms: the proportional/integral/derivative (PID) controllers, transfer function based (TFB) controllers, and state feedback (SF) controllers. The PID controller is defined by the equationu=KPe+KI∫e+KDė  (1)where u is the control signal and e is the error between the set point and the process output being controlled. This type of controller has been employed in engineering and other applications since the early 1920s. It is an error based controller that does not require an explicit mathematical model of the plant. The TFB controller is given in the form of
                                          U            ⁡                          (              s              )                                =                                                    G                c                            ⁡                              (                s                )                                      ⁢                          E              ⁡                              (                s                )                                                    ,                                  ⁢                                            G              c                        ⁡                          (              s              )                                =                                    n              ⁡                              (                s                )                                                    d              ⁡                              (                s                )                                                                        (        2        )            where U(s) and E(s) are Laplace Transforms of u and e defined above, and n(s) and d(s) are polynomials in s. The TFB controller can be designed using methods in control theory based on the transfer function model of the plant, Gp(s). A PID controller can be considered a special case of a TFB controller because it has an equivalent transfer function of
                                          G            c                    ⁡                      (            s            )                          =                              k            p                    +                                    k              i                        s                    +                                    k              d                        ⁢            s                                              (        3        )            The State Feedback (SF) Controller
The SF controller can be defined byu=r+K{circumflex over (x)}  (4)and is based on the state space model of the plant:{dot over (x)}(t)=Ax(t)+Bu(t),y(t)=Cx(t)+Du(t)  (5)When the state x is not accessible, a state observer (SO):{circumflex over ({dot over (x)}=A{circumflex over (x)}+Bu+L(y−ŷ)  (6)is often used to find its estimate, {circumflex over (x)}. Here r is the set point for the output to follow.Controller Tuning
Over the years, the advances in control theory provided a number of useful analysis and design tools. As a result, controller design moved from empirical methods (e.g., ad hoc tuning via Ziegler and Nichols tuning tables for PID) to analytical methods (e.g., pole placement). The frequency response method (Bode and Nyquist plots) also facilitated analytical control design.
Conventionally, controllers are individually designed according to design criteria and then individually tuned until they exhibit an acceptable performance. Practicing engineers may design controllers, (e.g., PID) using look-up tables and then tune the controllers using trial and error techniques. But each controller is typically individually designed, tuned, and tested.
Tuning controllers has perplexed engineers. Controllers that are developed based on a mathematical model of the plant usually need their parameters to be adjusted, or “tuned” as they are implemented in hardware and tested. This is because the mathematical model often does not accurately reflect the dynamics of the plant. Determining appropriate control parameters under such circumstances is often problematic, leading to control solutions that are functional but ill-tuned, yielding lost performance and wasted control energy.
Additionally, and/or alternatively, engineers design using analytical (e.g., pole placement) techniques, but once again tune with trial and error techniques. Since many industrial machines and engineering applications are built to be inherently stable, acceptable controllers can be designed and tuned using these conventional techniques, however, acceptable performance may not approach optimal performance.
One example conventional technique for designing a PID controller included obtaining an open-loop response and determining what, if anything, needed to be improved. By way of illustration, the designer would build a candidate system with a feedback loop, guess the initial values of the three gains (e.g., kp, kd, ki) in PID and observe the performance in terms of rise time, steady state error and so on. Then, the designer might modify the proportional gain to improve rise time. Similarly, the designer might add or modify a derivative controller to improve overshoot and an integral controller to eliminate steady state error. Each component would have its own gain that would be individually tuned. Thus, conventional designers often faced choosing three components in a PID controller and individually tuning each component. Furthermore, there could be many more parameters that the design engineer must tune if a TFB or a state feedback state observer (SFSOB) controller is employed.
Another observation of control design is that it is not portable. That is, each control problem is solved individually and its solution cannot be easily modified for another control problem. This means that the tedious design and tuning process must be repeated for each control problem. The use of state observers is useful in not only system monitoring and regulation but also detecting as well as identifying failures in dynamical systems. Since almost all observer designs are based on the mathematical model of the plant, the presence of disturbances, dynamic uncertainties, and nonlinearities pose great challenges in practical applications. Toward this end, the high-performance robust observer design problem has been topic of considerable interest recently, and several advanced observer designs have been proposed. Although satisfactory in certain respects, a need remains for an improved strategy for an observer and incorporation and use of such in a control system.
State Observers
Observers extract real-time information of a plant's internal state from its input-output data. The observer usually presumes precise model information of the plant, since performance is largely based on its mathematical accuracy. Closed loop controllers require both types of information. This relationship is depicted in 3200 of FIG. 32. Such presumptions, however, often make the method impractical in engineering applications, since the challenge for industry remains in constructing these models as part of the design process. Another level of complexity is added when gain scheduling and adaptive techniques are used to deal with nonlinearity and time variance, respectively.
Disturbance Estimation Observes and Disturbance Rejection
Recently, disturbance rejection techniques have been used to account for uncertainties in the real world and successfully control complex nonlinear systems. The premise is to solve the problem of model accuracy in reverse by modeling a system with an equivalent input disturbance d that represents any difference between the actual plant P and a derived/selected model Pn of the plant, including external disturbances w. An observer is then designed to estimate the disturbance in real time and provide feedback to cancel it. As a result, the augmented system acts like the model Pn at low frequencies, making the system accurate to Pn and allowing a controller to be designed for Pn. This concept is illustrated in 3900 of FIG. 39.
The most common of these techniques is the disturbance observer (DOB) structure (Endo, S., H. Kobayashi, C. J. Kempf, S. Kobayashi, M. Tomizuka and Y. Hori (1996). “Robust Digital Tracking Controller Design for High-Speed Positioning Systems.” Control Eng. Practice, 4:4, 527-536; Kim, B. K., H.-T. Choi, W. K. Chung and I. H. Suh (2002). “Analysis and Design of Robust Motion Controllers in the Unified Framework.” J. of Dynamic Systems, Measurement, and Control, 124, 313-321; Lee, H. S. and M. Tomizuka (1996). “Robust Motion Controller Design for High-Accuracy Positioning Systems.” IEEE Trans. Ind. Electron., 43:1, 48-55; Tesfaye, A., H. S. Lee and M. Tomizuka (2000). “A Sensitivity Optimization Approach to Design of a Disturbance Observer in Digital Motion Control.” IEEE/ASME Trans. on Mechatronics, 5:1, 32-38; Umeno, T. and Y. Hori (1991). “Robust Speed Control of DC Servomotors Using Modern Two Degrees of Freedom Controller Design”. IEEE Trans. Ind. Electron., 38:5, 363-368). It uses simple binomial Q-filters, allowing the observer to be parameterized, i.e. tuned by a single bandwidth parameter. A model deliberately different from P is also suggested in E. Schrijver and J. van Dijk, “Disturbance Observers for Rigid Mechanical Systems: Equivalence, Stability, and Design,” Journal of Dynamic Systems, Measurement, and Control, vol. 124, no. 4, pp. 539-548, 2002 to facilitate design, but no guidelines are given other than it should be as simple as possible, cautioning stability and performance may be in danger. Another obstacle is that a separate observer must be designed to provide state feedback to the controller. In existing research, derivative approximates are used in this way but their effect on performance and stability has yet to be analyzed. Furthermore, the controller design is dependent on the DOB design, meaning that derivative approximates can not be arbitrarily selected.
Multiple DOBs were used to control a multivariable robot by treating it as a set of decoupled single-input single-output (SISO) systems, each with disturbances that included the coupled dynamics (Bickel, R. and M. Tomizuka (1999). “Passivity-Based Versus Disturbance Observer Based Robot Control: Equivalence and Stability.” J. of Dynamic Systems, Measurement, and Control, 121, 41-47; Hori, Y., K. Shimura and M. Tomizuka (1992). “Position/Force Control of Multi-Axis Robot Manipulator Based on the TDOF Robust Servo Controller For Each Joint.” Proc. of ACC, 753-757; Kwon, S. J. and W. K. Chung (2002). “Robust Performance of the Multiloop Perturbation Compensator.” IEEE/ASME Trans. Mechatronics, 7:2, 190-200; Schrijver, E. and J. Van Dijk (2002) Disturbance Observers for Rigid Mechanical Systems: Equivalence, Stability, and Design.” J. of Dynamic Systems, Measurement, and Control, 124, 539-548.
Another technique, referred to as the unknown input observer (UIO), estimates the states of both the plant and the disturbance by augmenting a linear plant model with a linear disturbance model (Burl, J. B. (1999). Linear Optimal Control, pp. 308-314. Addison Wesley Longman, Inc., Calif.; Franklin, G. F., J. D. Powell and M. Workman (1998). Digital Control of Dynamic Systems, Third Edition, Addison Wesley Longman, Calif.; Johnson, C. D. (1971). “Accommodation of External Disturbances in Linear Regulator and Servomechanism Problems.” IEEE Trans. Automatic Control, AC-16:6, 635-644; Liu, C.-S., and H. Peng (2002). “Inverse-Dynamics Based State and Disturbance Observer for Linear Time-Invariant Systems.” J. of Dynamic Systems, Measurement, and Control, 124, 375-381; Profeta, J. A. III, W. G. Vogt and M. H. Mickle (1990). “Disturbance Estimation and Compensation in Linear Systems.” IEEE Trans. Aerospace and Electronic Systems, 26:2, 225-231; Schrijver, E. and J. van Dijk (2002) “Disturbance Observers for Rigid Mechanical Systems: Equivalence, Stability, and Design.” J. of Dynamic Systems, Measurement, and Control, 124, 539-548). Unlike the DOB structure, the controller and observer can be designed independently, like a Luenberger observer. However, it still relies on a good mathematical model and a design procedure to determine observer gains. An external disturbance w is generally modeled using cascaded integrators (1/sh). When they are assumed to be piece-wise constant, the observer is simply extended by one state and still demonstrates a high degree of performance.
Extended State Observer (ESO)
In this regard, the extended state observer (ESO) is quite different. Originally proposed by Han, J. (1999). “Nonlinear Design Methods for Control Systems.” Proc. 14th IFAC World Congress, in the form of a nonlinear UIO and later simplified to a linear version with one tuning parameter by Gao, Z. (2003). “Scaling and Parameterization Based Controller Tuning.” Proc. of ACC, 4989-4996, the ESO combines the state and disturbance estimation power of a UIO with the tuning simplicity of a DOB. One finds a decisive shift in the underlying design concept as well. The traditional observer is based on a linear time-invariant model that often describes a nonlinear time-varying process. Although the DOB and UIO reject input disturbances for such nominal plants, they leave the question of dynamic uncertainty mostly unanswered in direct form. The ESO, on the other hand, addresses both issues in one simple framework by formulating the simplest possible design model Pd=1/sn for a large class of uncertain systems. Pd is selected to simplify controller and observer design, forcing P to behave like it at low frequencies rather than Pn. As a result, the effects of most plant dynamics and external disturbances are concentrated into a single unknown quantity. The ESO estimates this quantity along with derivatives of the output, giving way to the straightforward design of a high performance controller.
Active Disturbance Rejection Control (ADRC)
Originally proposed by Han, J. (1999). “Nonlinear Design Methods for Control Systems.” Proc. 14th IFAC World Congress, a nonlinear, non-parameterized active disturbance rejection control (ADRC) is a method that uses an ESO. A linear version of the ADRC controller and ESO were parameterized for transparent tuning by Gao, Z. (2003). “Scaling and Parameterization Based Controller Tuning.” Proc. of ACC, 4989-4996. Its practical usefulness is seen in a number of benchmark applications already implemented throughout industry with promising results (Gao, Z., S. Hu and F. Jiang (2001). “A Novel Motion Control Design Approach Based on Active Disturbance Rejection.” Proc. of 40th IEEE Conference on Decision and Control; Goforth, F. (2004). “On Motion Control Design and Tuning Techniques.” Proc. of ACC; Hu, S. (2001). “On High Performance Servo Control Solutions for Hard Disk Drive.” Doctoral Dissertation, Department of Electrical and Computer Engineering, Cleveland State University; Hou, Y., Z. Gao, F. Jiang and B. T. Boulter (2001). “Active Disturbance Rejection Control for Web Tension Regulation.” Proc. of 40th IEEE Conf. on Decision and Control; Huang, Y., K. Xu and J. Han (2001). “Flight Control Design Using Extended State Observer and Nonsmooth Feedback.” Proc. of 40th IEEE Conf. on Decision and Control; Sun, B and Z. Gao (2004). “A DSP-Based Active Disturbance Rejection Control Design for a 1 KW H-Bridge DC-DC Power Converter.” To appear in: IEEE Trans. on Ind. Electronics; Xia, Y., L. Wu, K. Xu, and J. Han (2004). “Active Disturbance Rejection Control for Uncertain Multivariable Systems With Time-Delay, 2004 Chinese Control Conference). It was also applied to a fairly complex multivariable aircraft control problem (Huang, Y., K. Xu and J. Han (2001). “Flight Control Design Using Extended State Observer and Nonsmooth Feedback.” Proc. of 40th IEEE Conf. on Decision and Control).
What is needed is a control framework for application to systems throughout industry that are complex and largely unknown to the personnel often responsible for controlling them. In the absence of required expertise, less tuning parameters are needed than current approaches, such as multi-loop PID, while maintaining or even improving performance and robustness.
Linear Active Disturbance Rejection Controller (LADRC)
In addition to the above controllers, a more practical controller is the recently developed from Active Disturbance Rejection Controller (ADRC). Its linear form (LADRC) for a second order plant is introduced below as an illustration. The unique distinction of ADRC is that it is largely independent of the mathematical model of the plant and is therefore better than most controllers in performance and robustness in practical applications.
Consider an example of controlling a second order plantÿ=−a{dot over (y)}−by +w+bu  (7)where y and u are output and input, respectively, and w is an input disturbance. Here both parameters, a and b, are unknown, although there is some knowledge of b, (e.g., b0≈b, derived from the initial acceleration of y in step response). Rewrite (7) asÿ=−a{dot over (y)}−by+w+(b−b0)u+b0u=ƒ+b0u  (8)where ƒ=−a{dot over (y)}−by+w+(b−b0)u. Here ƒ is referred to as the generalized disturbance, or disturbance, because it represents both the unknown internal dynamics, −a{dot over (y)}−by+(b−b0)u and the external disturbance w(t).
  u  =                              -                      f            ^                          +                  u          0                    ⁢                                  b      0      
If an estimate of ƒ, {circumflex over (ƒ)} can be obtained, then the control law reduces the plant to ÿ=(ƒ−{circumflex over (ƒ)})+u0 which is a unit-gain double integrator control problem with a disturbance (ƒ−{circumflex over (ƒ)}).
Thus, rewrite the plant in (8) in state space form as
                    {                                                                            ⁢                                                                            x                      .                                        1                                    =                                      x                    2                                                                                                                                                                                                            ⁢                      x                                        .                                    2                                =                                                      x                    3                                    +                                                            b                      0                                        ⁢                    u                                                                                                                                                                                                            ⁢                      x                                        .                                    3                                =                h                                                                                                        ⁢                                  y                  =                                      x                    1                                                                                                          (        9        )            with x3=ƒ added as an augmented state, and h={dot over (ƒ)} is seen as an unknown disturbance. Now ƒ can be estimated using a state observer based on the state space model
                                                                                                            ⁢                  x                                .                            =                              Ax                +                Bu                +                Eh                                                                                                      ⁢                              y                =                Cz                                                                          where                                                                              A                =                                  ⌊                                                                                    0                                                                    1                                                                    0                                                                                                            0                                                                    0                                                                    1                                                                                                            0                                                                    0                                                                    0                                                                              ⌋                                            ,                              B                =                                  ⌊                                                                                    0                                                                                                                                      b                          0                                                                                                                                    0                                                                              ⌋                                            ,                              C                =                                  [                                                                                    1                                                                    0                                                                                                                          0                            ]                                                    ,                                                      E                            =                                                          ⌊                                                                                                                                    0                                                                                                                                                                        0                                                                                                                                                                        1                                                                                                                                                                                                                                                            ⌋                                                                                        (        10        )            Now the state space observer, denoted as the linear extended state observer (LESO), of (10) can be constructed asż=Az+Bu+L(y−ŷ)ŷ=Czand if ƒ is known or partially known, it can be used in the observer by taking h={dot over (ƒ)} to improve estimation accuracy.ż=Az+Bu+L(y−ŷ)+Eh ŷ=Cz  (11a)The observer can be reconstructed in software, for example, and L is the observer gain vector, which can be obtained using various methods known in the art like pole placement,L=[β1β2β3]T  (12)where [ ]T denotes transpose. With the given state observer, the control law can be given as:
                    u        =                                            -                              z                3                                      +                          u              0                                            b            0                                              (        13        )            Ignoring the inaccuracy of the observer,ÿ=(ƒ−z3)+u0≈u0  (14)which is an unit gain double integrator that can be implemented with a PD controlleru0=kp(r−z1)−kdz2  (15)Tracking Control
Command following refers to the output of a controlled system meeting design requirements when a specified reference trajectory is applied. Oftentimes, it refers to how closely the output y compares to the reference input r at any given point in time. This measurement is known as the error e=r−y.
Control problems can be categorized in two major groups; point-to-point control and tracking control. Point-to-point applications call for a smooth step response with minimal overshoot and zero steady state error, such as when controlling linear motion from one position to the next and then stopping. Since the importance is placed on destination accuracy and not on the trajectory between points, conventional design methods produce a controller with inherent phase lag in order to produce a smooth output. Tracking applications require precise tracking of a reference input by keeping the error as small as possible, such as when controlling a process that does not stop. Since the importance is placed on accurately following a changing reference trajectory between points, the problem here is that any phase lag produces unacceptably large errors in the transient response, which lasts for the duration of the process. Although it does not produce a response without overshoot, it does produce a much smaller error signal than the point-to-point controller. The significance is in its ability to reduce the error by orders of magnitude. A step input may be used in point-to-point applications, but a motion profile should be used in tracking applications.
Various methods have been used to remove phase lag from conventional control systems. All of them essentially modify the control law to create a desired closed loop transfer function equal to one. As a result, the output tracks the reference input without any phase lag and the effective bandwidth of the overall system is improved. The most common method is model inversion where the inverse of the desired closed loop transfer function is added as a prefilter. Another method proposed a zero Phase Error Tracking Controller (ZPETC) that cancels poles and stable zeros of the closed loop system and compensates for phase error introduced by un-cancelable zeros. Although it is referred to as a tracking controller, it is really a prefilter that reduces to the inverse of the desired closed loop transfer function when unstable zeros are not present. Other methods consist of a single tracking control law with feed forward terms in place of the conventional feedback controller and prefilter, but they are application specific. However, all of these and other previous methods apply to systems where the model is known.
Model inaccuracy can also create tracking problems. The performance of model-based controllers is largely dependent on the accuracy of the model. When linear time-invariant (LTI) models are used to characterize nonlinear time-varying (NTV) systems, the information becomes inaccurate over time. As a result, gain scheduling and adaptive techniques are developed to deal with nonlinearity and time variance, respectively. However, the complexity added to the design process leads to an impractical solution for industry because of the time and level of expertise involved in constructing accurate mathematical models and designing, tuning, and maintaining each control system.
There have been a number of high performance tracking algorithms that consist of three primary components: disturbance rejection, feedback control, and phase error compensation implemented as a prefilter. First, disturbance rejection techniques are applied to eliminate model inaccuracy with an inner feedback loop. Next, a stabilizing controller is constructed based on a nominal model and implemented in an outer feedback loop. Finally, the inverse of the desired closed loop transfer function is added as a prefilter to eliminate phase lag. Many studies have concentrated on unifying the disturbance rejection and control part, but not on combining the control and phase error compensation part, such as the RIC framework. Internal model control (IMC) cancels an equivalent output disturbance. B. Francis and W. Wonham, “The Internal Model Principal of Control Theory,” Automatica, vol 12, 1976, pp. 457-465. E. Schrijver and J. van Dijk, “Disturbance Observers for Rigid Mechanical Systems Equivalence, Stability, and Design,” Journal of Dynamic Systems, Measurement, and Control, vol. 124, December 2002, pp. 539-548 uses a basic tracking controller with a DOB to control a multivariable robot. The ZPETC has been widely used in combination with the DOB framework and model based controllers.
Thus, having reviewed controllers and observers, the application now describes example systems and methods related to controllers and observers.
Web Processing Applications
Web tension regulation is a challenging industrial control problem. Many types of material, such as paper, plastic film, cloth fabrics, and even strip steel are manufactured or processed in a web form. The quality of the end product is often greatly affected by the web tension, making it a crucial variable for feedback control design, together with the velocities at the various stages in the manufacturing process. The ever-increasing demands on the quality and efficiency in industry motivate researchers and engineers alike to explore better methods for tension and velocity control. However, the highly nonlinear nature of the web handling process and changes in operating conditions (temperature, humidity, machine wear, and variations in raw materials) make the control problem challenging.
Accumulators in web processing lines are important elements in web handling machines as they are primarily responsible for continuous operation of web processing lines. For this reason, the study and control of accumulator dynamics is an important concern that involves a particular class of problems. The characteristics of an accumulator and its operation as well as the dynamic behavior and control of the accumulator carriage, web spans, and tension are known in the art.
Both open-loop and closed-loop methods are commonly used in web processing industries for tension control purposes. In the open-loop control case, the tension in a web span is controlled indirectly by regulating the velocities of the rollers at either end of the web span. An inherent drawback of this method is its dependency on an accurate mathematical model between the velocities and tension, which is highly nonlinear and highly sensitive to velocity variations. Nevertheless, simplicity of the controller outweighs this drawback in many applications. Closing the tension loop with tension feedback is an obvious solution to improve accuracy and to reduce sensitivity to modeling errors. It requires tension measurement, for example, through a load cell, but is typically justified by the resulting improvements in tension regulation.
Most control systems will unavoidably encounter disturbances, both internal and external, and such disturbances have been the obstacles to the development of high performance controller. This is particularly true for tension control applications and, therefore, a good tension regulation scheme must be able to deal with unknown disturbances. In particular, tension dynamics are highly nonlinear and sensitive to velocity variations. Further, process control variables are highly dependent on the operating conditions and web material characteristics. Thus, what are needed are systems and methods for control that are not only overly dependent on the accuracy of the plant model, but also suitable for the rejection of significant internal and external disturbances.
Jet Engine Control Applications
A great deal of research has been conducted towards the application of modern multivariable control techniques on aircraft engines. The majority of this research has been to control the engine at a single operating point. Among these methods are a multivariable integrator windup protection scheme (Watts, S. R. and S. Garg (1996). “An Optimized Integrator Windup Protection Technique Applied to a Turbofan Engine Control,” AIAA Guidance Navigation and Control Conf.), a tracking filter and a control mode selection for model based control (Adibhatla S. and Z. Gastineau (1994). “Tracking Filter Selection And Control Mode Selection For Model Based Control.” AIAA 30th Joint Propulsion Conference and Exhibit), an Hm method and linear quadratic Gaussian with loop transfer recovery method (Watts, S. R. and S. Garg (1995). “A Comparison Of Multivariable Control Design Techniques For A Turbofan Engine Control.” International Gas Turbine and Aeroengine Congress and Expo.), and a performance seeking control method (Adibhatla, S. and K. L. Johnson (1993). “Evaluation of a Nonlinear Psc Algorithm on a Variable Cycle Engine.” AIAA/SAE/ASME/ASEE 29th Joint Propulsion Conference and Exhibit). Various schemes have been developed to reduce gain scheduling (Garg, S. (1997). “A Simplified Scheme for Scheduling Multivariable Controllers.” IEEE Control Systems) and have even been combined with integrator windup protection and Hm (Frederick, D. K., S. Garg and S. Adibhatla (2000). “Turbofan Engine Control Design Using Robust Multivariable Control Technologies. IEEE Trans. on Control Systems Technology).
Conventionally, there have been a limited number of control techniques for full flight operation (Garg, S. (1997). “A Simplified Scheme for Scheduling Multivariable Controllers.” IEEE Control Systems; and Polley, J. A., S. Adibhatla and P. J. Hoffman (1988). “Multivariable Turbofan Engine Control for Full Conference on Decision and Control Flight Operation.” Gas Turbine and Expo). However, there has been no development of tuning a controller for satisfactory performance when applied to an engine. Generally, at any given operating point, models can become inaccurate from one engine to another. This accuracy increases with model complexity, and subsequently design and tuning complexity. As a result, very few of these or similar aircraft design studies have led to implementation on an operational vehicle.
The current method for controlling high performance jet engines remains multivariable proportional-integral (PI) control (Edmunds, J. M. (1979). “Control System Design Using Closed-Loop Nyquist and Bode Arrays.” Int. J on Control, 30:5, 773-802, and Polley, J. A., S. Adibhatla and P. J. Hoffman (1988). “Multivariable Turbofan Engine Control for Full Conference on Decision and Control. Flight Operation.” Gas Turbine and Expo). Although the controller is designed by implementing Bode and Nyquist techniques and is tunable, a problem remains due to the sheer number of tuning parameters compounded by scheduling.
Health Monitoring and Fault Detection
The terms “health”, “fault”, “diagnosis”, and “tolerance” are used in broad terms. Some literature defines a fault as an unpermitted deviation of at least one characteristic property or variable by L. H. Chiang, E. Russell, and R. D. Braatz, Fault Detection and Diagnosis in Industrial Systems, Springer-Verlag, February 2001. Others define it more generally as the indication that something is going wrong with the system by J. J. Gertler, “Survey of model-based failure detection and isolation in complex plants,” IEEE Control Systems Magazine, December 1988.
Industry is increasingly interested in actively diagnosing faults in complex systems. The importance of fault diagnosis can be seen by the amount of literature associated with it. There are a number of good survey papers by (J. J. Gertler, “Survey of model-based failure detection and isolation in complex plants,” IEEE Control Systems Magazine, December 1988. V. Venkatasubramanian, R. Rengaswamy, K. Yin, and S. N. Kavuri, “A review of process fault detection and diagnosis part i: Quantitative model-based methods,” Computers and Chemical Engineering, vol. 27, pp. 293-311, April 2003, (P. M. Frank, “Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: a survey and some new results,” Automatica, vol. 26, no. 3, pp. 459-474, 1990, K. Madani, “A survey of artificial neural networks based fault detection and fault diagnosis techniques,” International Joint Conference on Neural Networks, vol. 5, pp. 3442-3446, July 1999, P. M. Frank, “Analytical and qualitative model-based fault diagnosis-a survey and some new results,” European Journal of Control, 1996, P. M. Frank and X. Ding, “Survey of robust residual generation and evaluation methods in observer-based fault detection,” Journal of Process Control, 1997, J. Riedesel, “A survey of fault diagnosis technology [for space power systems],” in Proceedings of the 24th Intersociety IECEC-89. Conversion Engineering Conference, 1989, pp. 183-188, A. Willsky, “A survey of design methods for failure detection in dynamic systems,” NASA STI/Recon Technical Report N, vol. 76, pp. 11 347-+, 1975, M. Kinnaert, “Fault diagnosis based on analytical models for linear and nonlinear systems—a tutorial,” Department of Control Engineering and System Analysis, Université Libre de Bruxelles, Tech. Rep., 2004.) and books by (L. H. Chiang, E. Russell, and R. D. Braatz, Fault Detection and Diagnosis in Industrial Systems, Springer-Verlag, February 2001, M. Blanke, M. Kinnaert, J. Junze, M. Staroswiecki, J. Schroder, and J. Lunze, Diagnosis and Fault-Tolerant Control, Springer-Verlag, August 2003, R. Patton, P. M. Frank, and R. N. Clark, Issues of Fault Diagnosis for Dynamic Systems, Springer-Verlag Telos, 2000, S. Simani, C. Fantuzzi, and R. Patton, Model-based Fault Diagnosis in Dynamic Systems Using Identification Techniques. Springer-Verlag, January 2003, E. Russell, L. H. Chiang, and R. D. Braatz, Data-Driven Methods for Fault Detection and Diagnosis in Chemical Processes (Advances in Industrial Control). Springer-Verlag, 2000, M. Basseville and I. V. Nikiforov, Detection of Abrupt Changes: Theory and Application. Prentice-Hall, Inc, April 1993.) which collect many of the issues and solutions for faults.
There are four main categories of fault diagnosis. Fault detection is the indication that something is going wrong with the system. Fault isolation determines the location of the failure. Failure identification is the determination of the size of the failure. Fault accommodation and remediation is the act or process of correcting a fault. Most fault solutions deal with the first three categories and do not make adjustments to closed loop systems. The common solutions can be categorized into a six major areas:                1. Analytical redundancy by (J. J. Gertler, “Survey of model-based failure detection and isolation in complex plants,” IEEE Control Systems Magazine, December 1988, A. Willsky, “A survey of design methods for failure detection in dynamic systems,” NASA STI/Recon Technical Report N, vol. 76, pp. 11 347-+, 1975, E. Y. Chow and A. S. Willsky, “Analytical redundancy and the design of robust failure detection systems,” IEEE Transactions on Automatic Control, October 1982.)        2. Statistical analysis by (L. H. Chiang, E. Russell, and R. D. Braatz, Fault Detection and Diagnosis in industrial Systems, Springer-Verlag, February 2001, E. Russell, L. H. Chiang, and R. D. Braatz, Data-Driven Methods for Fault Detection and Diagnosis in Chemical Processes (Advances in Industrial Control). Springer-Verlag, 2000, M. Basseville and I. V. Nikiforov, Detection of Abrupt Changes: Theory and Application. Prentice-Hall, Inc, April 1993.)        3. Knowledge/fuzzy logic systems        4. Neural networks by (K. Madani, “A survey of artificial neural networks based fault detection and fault diagnosis techniques,” International Joint Conference on Neural Networks, vol. 5, pp. 3442-3446, July 1999, J. W. Hines, D. W. Miller, and B. K. Hajek, “Fault detection and isolation: A hybrid approach,” in American Nuclear Society Annual Meeting and Embedded Topical Meeting on Computer-Based Human Support Systems Technology, Methods and Future, Philadelphia, Pa., Oct. 29-Nov. 2 1995.)        5. Hybrid solutions by (J. W. Hines, D. W. Miller, and B. K. Hajek, “Fault detection and isolation: A hybrid approach,” in American Nuclear Society Annual Meeting and Embedded Topical Meeting on Computer-Based Human Support Systems: Technology, Methods and Future, Philadelphia, Pa., Oct. 29-Nov. 2 1995.)        6. Fault tolerant control by (M. Kinnaert, “Fault diagnosis based on analytical models for linear and nonlinear systems—a tutorial,” Department of Control Engineering and System Analysis, Université Libre de Bruxelles, Tech. Rep., 2004, M. Blanke, M. Kinnaert, J. Junze, M. Staroswiecki, J. Schroder, and J. Lunze, Diagnosis and Fault-Tolerant Control, Springer-Verlag, August 2003)        
Some of these methods attempt to remove the need for accurate mathematical models yet require other implicit models. Analytical redundancy by (E. Y. Chow and A. S. Willsky, “Analytical redundancy and the design of robust failure detection systems,” IEEE Transactions on Automatic Control, October 1982.), the most popular method, relies heavily on mathematical models.
Often detailed model information is not available although diagnostics of the dynamic control system are still important. A less developed but important problem is characterizing what can be determined from input output data with few assumptions about the plant.
Without adequate knowledge of the plant, disturbances, faults, and modeling errors, it is difficult to build an effective estimator. For the most part, each of these issues has been approached independently.